"Time remap" or slow speed of cloth particles driven by a force
Final:



Overview:

This is pretty easy solution surprisingly. Only thing you need to do is keyframing Cloth > Speed > Multiplier value.


  Slow down speed is exaggerated in this example just to be more
  visible. For slowing down by 15% use values 0.75 instead of 0.1.


Steps:


Set frame to 1 and press I hovering mouse cursor over Multiplier value 1 to set keyframe.
Select next frame which should be starting point for slow down, change Multiplier to something like 0.1 (smaller value, slower time) and set keyframe.
Select frame which should be start of the end of slow down and set another 0.1 Multiplier keyframe.
Lastly set a keyframe which will be definite end of the slow down with Multiplier value 1.


If you want so more help, please put it in the comments as I really don't know what else to explain, it's really simple setup.



Edit:

As @risingfall stated in his comment, you will need to add new cache to Particles and set Cache step to 1, than remove previous one and do the same with Cloth (without changing step, as it isn't present).



Edit 2:

It seems that doing this only with Cloth cache is enough. Even in my gif under final you can see that on the timeline sim is baked only at certain frames. Adding and deleting cache for Cloth is fixing this. To be sure, re-add both caches.

I don't know why this is happening, I'm gonna investigate it further, but at a first glance it seems to be bug/corrupted cache.